I beg to disagree: For buying, because of limited risk, asymmetric returns but low probability of success, I need to make large number of bets, enough so I can meet my statistically significant probability calculation of wins, in order to collect enough big hits, to meet my expectancy. Think venture investing. For writing, because of limited gain but unlimited risks, I would be more careful in placing my bets. To avoid getting one huge loss that wipe me out and to have a big enough payout when I am right, I need to leverage big but place very few bets. Think Russian roulette. But, 99% of the folks on ET would disagree with me and would not trade this way.
You don't approximate brownian motion. It is a theory on how stocks move (geometric brownian motion to be exact). This motion is what is assumed when pricing options. If you think a stock will trend in one direction the OTM calls and puts will most likely be under priced (assuming no delta hedging because you are just trading the terminal distribution ie. where the stock is now vs where it will be at expiration).
I am not trying to approximate. The stock price behavior could be a combination of a brownian, a drift + .... Brownian ~ SQRT (T), drift ~ T so when T is short, brownian dominates drift and the price is mostly Gaussian?
Try SPY Weekly's, Monday, Wed, Fri. expirations. Long ATM Call when breakout from pivot high, Tues only, LX +.80, LXstop -.70 ATM put pivot low breakout, Wed and Fri only, LX +1.0, LXstop -.70
Currently Strangles on earnings but cheap 2 days ahead or more. Run TOS scan any large volume calls 30 to 45 days out cheap. Fridays on weeklies just itm calls with good upside. Looking at doing short iron butterflies atm
Right now this is all I’m doing: -Sell cash covered puts for stocks I want to buy at my price. -Sell covered calls on stocks I want to sell at my price. -Usually about 1 to 2 weeks out. It’s just a way to pick up extra cash on a stock trade instead of a limit order. I will sell out of the money covered calls on a select few of my positions 1 to 2 weeks out avoiding earnings, ex-div dates and exogenous events (as well as can be predicted for a particular stock). I have been called out at times, but the calls were far enough out that I could get back in below the strike when the underlying retraced. Overall, it’s a conservative way to supplement my stock investments, not an option trading strategy per se.